David Cameron today pledged to deliver a dramatic redistribution of power "from elites in Whitehall to the man and woman on the street" as he set out his plans to create what the Tories are calling the "big society".

In his most important speech since the general election on the devolution of power, the prime minister said he wanted to create communities with "oomph" and end the days in which capable people become "passive recipients" of state help.

Delivering the speech in Liverpool, he denied the programme was a mask for public sector cuts.

"The big society ... is about liberation – the biggest, most dramatic redistribution of power from elites in Whitehall to the man and woman on the street," the prime minister said.

"And this is such a powerful idea for blindingly obvious reasons. For years, there was the basic assumption at the heart of government that the way to improve things in society was to micromanage from the centre, from Westminster. But this just doesn't work."

Liverpool will be one of four "vanguard" areas that will receive special help to set up projects, ranging from local transport to improving the provision of broadband. The other areas are Eden Valley in Cumbria, Windsor and Maidenhead, and Sutton.

Cameron said that the vanguard communities, each to be given a team of civil servants, will be the "training grounds" of the 'big society'. In Liverpool, a volunteer programme is being built to keep museums open for longer.

In Cumbria, the new Tory MP for Penrith and the Borders, Rory Stewart, is trying to improve the provision of broadband.

The prime minister made a point of outlining tangible examples of benefits from the "big society" as he answered critics who said during the election that the idea was vague. Shadow ministers claimed the idea was impossible to sell on the doorstep, with one complaining that the term sounded like "Hegelian dialectic" dreamed up by Oliver Letwin.

A "big society" bank will be established to finance charities and voluntary groups. This will be funded using "every penny of dormant bank and building society account money allocated to England", Cameron announced.

He said it would eventually allocate hundreds of millions of pounds. But the Financial Times reported today that the bank would only be able to launch with reserves of around £60m.

Cameron also outlined three strands of what he called the "Big Society" agenda:

• Social action: "Government ... must foster and support a new culture of voluntarism, philanthropy, social action."

• Public service reform: "We've got to get rid of the centralised bureaucracy that wastes money and undermines morale."

• Community empowerment: "We need to create communities with oomph – neighbourhoods who are in charge of their own destiny, who feel if they club together and get involved they can shape the world around them."

Cameron insisted the "big society" idea was simple as he reminded his audience at Liverpool Hope University that he has been talking about it since he stood for the Tory leadership in 2005.

"The big society is about a huge culture change where people in their everyday lives, in their homes, their neighbourhoods and their workplace don't always turn to officials, local authorities or central government for answers to the problems they face. But instead they will feel both free and powerful enough to help themselves and their own communities."

Cameron conceded that it would be naive to assume that society will miraculously spring up if government rolls back. Government is needed to help devolve power, he said, as he called for a new approach from Whitehall.

"The truth is that we need a government that actually helps to build up the big society. This means a whole new approach to government and governing.

"For a long time the way government has worked – top-down, top-heavy, controlling – has frequently had the effect of sapping responsibility, local innovation and civic action. It has turned many motivated public sector workers into disillusioned, weary puppets of government targets.

"It has turned able, capable individuals into passive recipients of state help with little hope for a better future. It has turned lively communities into dull, soulless clones of one another. So we need to turn government completely on its head."

Earlier, Cameron today denied that his "big society" agenda was a cover for public service cuts.

He said: "It is not a cover for anything. I was talking about the "big society" and encouraging volunteering, encouraging social enterprises and voluntary groups to do more to make our society stronger. I was talking about that way before we had a problem with cuts and deficits and all the rest of it.

"This would be a great agenda whether we were having to cut public spending or whether we were increasing public spending."

He told BBC Breakfast: "This is not about trying to save money, it is about trying to have a bigger, better society."

Responding for Labour, Tessa Jowell, shadow Cabinet Office minister, said: "The content of today's speech is simply a brass-necked rebranding of programmes already put in place by a Labour government. Funding for a social investment bank and community pubs was put in place in March, and residents have been involved in setting council budgets for a number of years."

Dave Prentis, the general secretary of Unison, which represents many public sector workers, said: "Make no mistake, this plan is all about saving money, and it will cost even more jobs and lead to more service cuts. The government is simply washing its hands of providing decent public services and using volunteers as a cut-price alternative."

The Labour leadership contender Ed Miliband yesterday accused the Conservative party of "cynically attempting to dignify its cuts agenda, by dressing up the withdrawal of support with the language of reinvigorating civic society".

He said: "People in the voluntary sector know that, for all the talk of a big society, what is actually on the way is cuts and the abandonment of community projects across Britain.

"Make no mistake, under the Tories the voluntary sector's role will be shrunk, not expanded."